A frayed or snapped cable on a residential door is under real tension, and on a door from the 1969-1988 build window, the torsion spring holding that tension has usually never been replaced. Pulling a broken cable off a drum without releasing that spring first is how people get hurt. If your door is a single panel and the cable came off a pulley on an extension-spring setup, the risk is lower, but you're still working above a door that can drop.
The honest answer: replacing a cable yourself is possible if you've done it before and you own the right winding bars. If you haven't, it's not the place to learn. We'd rather talk you through what's broken over the phone and come handle it than have you find out the hard way what a loaded torsion spring does when it lets go. This is also where the area's housing age cuts both ways - older torsion hardware is usually simple and well understood, but the spring tension on a door that's sat since the early 80s with the original spring is higher risk, not lower, because the spring itself is overdue regardless of the cable.